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I'm curious about the references to "set builder" notation that I see in forum posts. Is this now a popular method of teaching elementary set theory and writing elementary proofs?

I haven't looked at materials for that subject in the past 20 years. The use of the "A = {x:....}" type of notation is very old, but in some posts I see that people are encouraged to write proofs that consist exclusively of "steps" that use that notation. Unlike the old fashioned "steps and reasons" form of proof used in secondary school, these "set builder" "proofs" often don't give a reason for each step.

The specialized methods used by the educational community to do proofs are compromises between two goals. 1. Having the student demonstrate an understanding of the material. 2. Using a format that is easy to grade ! These two goals are somewhat at odds with each other. Things that are easy to grade tend to be abbreviated and sometimes students who don't competely understand what they are doing can still write down the right symbols. However, compromises must be made in teaching classes. It seems to me that proofs in "set builder" notation are such a compromise.

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# Set builder notation and proofs

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